Productivity features
Simple, easy to use OO interface designed to minimise the effort required to render 3D scenes, and to be independent of 3D implementation e.g. Direct3D, OpenGL, Glide etc.
Extensible example framework makes getting your application running is quick and simple.
Common requirements like render state management, hierarchical culling, dealing with transparency are done for you automatically saving you valuable time.
Clean, uncluttered design and full documentation of all engine classes.
Fully OO design allows you to extend the engine's functionality through plugins and subclasses with very little effort.

Platform & 3D API support
Direct3D (Supporting DirectX 7 and 9) and OpenGL support [Note:DirectX 7 Unsupported as of Ogre 1.2.0].
Windows (all major versions), Linux and Mac OSX support
Builds on Visual C++ 6, Visual C++ .NET, Visual C++ .NET 2003 and Visual C++ 2005 on Windows (STLport required for Visual C++ versions prior to 2003) [Note: Visual C++ 6 / Visual C++ 7.0 deprecated as of Ogre 1.2.0].
Builds on gcc 3+ on Linux and Mac OSX

Material / Shader support
Powerful material declaration language allows you to maintain material assets outside of your code
Supports vertex and fragment programs (shaders), both low-level programs written in assembler, and high-level programs written in: Cg, Direct X 9 HLSL, or OpenGL GLSL. Provides automatic support for many commonly bound constant parameters like worldview matrices, light state information, object space eye position etc
Supports the complete range of fixed function operations such as multitexture and multipass blending, texture coordinate generation and modification, independent colour and alpha operations for non-programmable hardware or for lower cost materials
Multiple pass effects, with pass iteration if required for the closest 'n' lights
Support for multiple material techniques means you can design in alternative effects for a wide range of cards and OGRE automatically uses the best one supported
Material LOD support; your materials can reduce in cost as the objects using them get further away
Load textures from PNG, JPEG, TGA, BMP or DDS files, including unusual formats like 1D textures, volumetric textures, cubemaps, HDR (high dynamic range) and compressed textures (DXT/S3TC)
Support for dynamic textures in all supported formats, for efficient playback of movies and other realtime content on a texture

Meshes
Flexible mesh data formats accepted, separation of the concepts of vertex buffers, index buffers, vertex declarations and buffer mappings
Export from many modelling tools including Milkshape3D, 3D Studio Max, Maya, Blender and Wings3D
Skeletal animation, including blending of multiple animations and variable bone weight skinning
Biquadric Bezier patches for curved surfaces
Progressive meshes (LOD)
OpenGL Style Primitive Creation

Scene Features
Highly customisable, flexible scene management, not tied to any single scene type. Use predefined classes for scene organisation if they suit or plug in your own subclass to gain full control over the scene organisation. While other engines are limited due to the fact that they are geared towards a specific scene type, OGRE allows you to efficiently render any type of scene you can conceive.
Generic SceneManager hierarchically culls by bounding volumes
BSP-based plugin allows fast indoor renders, loading Quake3 levels inc. shader script parsing support
Octree plugin allows you to cull generic scenes based on an octree
Terrain plugin allows you to render geo-mipmapped terrains
Hierarchical scene graph; nodes allow objects to be attached to each other and follow each others movements, articulated structures etc
Set up spline paths for scene objects, including entities and cameras, which can then be animated easily

Special Effects
Particle Systems, including easily extensible emitters and affectors (customisable through plugins). Systems can be defined in text scripts for easy tweaking. Automatic use of particle pooling for maximum performance
Support for skyboxes, skyplanes and skydomes, very easy to use
Billboarding for sprite graphics
Transparent objects automatically managed (rendering order & depth buffer settings all set up for you)
Overlay system allow you to build HUDs and menus using 2D or 3D objects
Flexible fog control
Software dot3 bump mapping
Cube mapping
Post-processing Effects

Misc features
Common resource infrastructure for memory management and loading from archives (ZIP, PK3)
Flexible plugin architecture allows engine to be extended without recompilation
'Controllers' allow you to easily organise derived values between objects e.g. changing the colour of a ship based on shields left
Debugging memory manager for identifying memory leaks
XMLConverter to convert efficient runtime binary formats to/from XML for interchange or editing
Initializing Ogre with custom GPU capabilities to test and tweak your OGRE application as it would appear on older hardware.
Framework for integration with other libraries such as physics and collision via the ReferenceAppLayer, allowing you to tie the OGRE world geometry to the physics and collision libraries of your choice. This gives you the flexibility to use the libraries that are right for you, rather than being constricted to a single library. Many people are already using ODE and Tokamok (via Ogretok) for physics, and ODE or OPCODE for collisions, but you can use any library you would like.